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- Title
nOn The Diophantine Equation (132k)<sup>x</sup> + (4355k)<sup>y</sup> = (4357k)<sup>z</sup>.
- Authors
Balfaqih, Abdulrahman; Kamarulhaili, Hailiza
- Abstract
The Jeśmanowicz's conjecture written in 1956 states that for any primitive Pythagorean triple (a, b, c) with a2+b2 = c2 and any positive integer k, the only solution of equation (ak)x+(bk)y = (ck)z in positive integers is (x, y, z) = (2, 2, 2). In this paper, we show that the special Diophantine equation (132k)x + (4355k)y = (4357k)z has the only positive integer solution (x, y, z) = (2, 2, 2) for every positive integer k.
- Subjects
DIOPHANTINE equations; INTEGERS
- Publication
International Journal of Mathematics & Computer Science, 2019, Vol 14, Issue 4, p775
- ISSN
1814-0424
- Publication type
Article